The phenomena of electricity and magnetism, beta decay in radioactive nuclei, and the confinement of quarks within the proton can each be explained using the three different gauge theories which collectively make up the standard model. Alternative gauge theories display new kinds of exotic phenomena, which are not fully understood. For example, if the field content is chosen appropriately, a gauge theory is said to be in the conformal window, and can acquire conformal symmetry. In this case, all fundamental mass scales vanish from the theory and its states no longer correspond to collections of particles. This thesis focuses on nearly conformal gauge theories, which have a field content chosen to place them just outside of the conformal window. They exhibit confinement at low energies, but numerical studies indicate that their properties differ markedly from the familiar gauge theories of the standard model. In particular, an anomalously light composite scalar forms in these theories, which could be a Higgs boson candidate that would resolve the standard model hierarchy problem.
Revealing the variety of phenomena exhibited by nearly conformal gauge theories is challenging because these theories confine, are strongly coupled and therefore cannot be analyzed using the standard tools of perturbation theory. Lattice gauge theory has been used to study these theories numerically. These studies have revealed a wealth of useful information about the nearly conformal gauge theories, including the presence of a light scalar composite state in the spectrum, but they required significant computer resources, so having complimentary theoretical tools would be advantageous.
To this end, two effective field theories (EFTs) are developed in this thesis: A dilaton EFT in which the lightest scalar state is interpreted as a pseudo–Goldstone boson arising from the spontaneous breaking of conformal symmetry, and a linear sigma EFT, in which the lightest scalar belongs to a multiplet of states transforming linearly under an internal symmetry. These weakly coupled EFTs include only the lightest degrees of freedom present in the spectrum of the gauge theories and provide a simple, approximate description of the same physics, enabling extrapolation of the lattice results to regions of parameter space that are otherwise inaccessible. The dilaton EFT is fitted to lattice data with encouraging results.
Thesis Advisor: Thomas Appelquist (thomas.appelquist@yale.edu)